(1) Field of the Invention
This invention is related to cost-optimal state feedback control systems and more particularly to a "region" control system which regulates or stabilizes the inertial platform of a vehicle in motion and which has computational requirements within the capability of the vehicle onboard control processors.
(2) Statement of Prior Art
Vehicle inertial reference subsystems contain a gyrostabilized platform which is instrumented with accelerometers that are used to sense the vehicle motion along three orthogonal axes. The vehicle guidance computer uses the data from these accelerometers to determine the vehicle position and the velocity vectors which in turn are used for computing the vehicle steering commands. The navigation problem is to determine the acceleration of the vehicle along axes that define a three dimensional space which is established prior to flight and is fixed during the entire flight. Therefore, the platform on which the accelerometers are mounted must be suspended in inertial space during the flight and must remain unperturbed by the vehicle motion. A mechanical assembly of four concentric gimbals is used to isolate the inertial platform from its environment. The innermost gimbal, or stable member (which is also known as elevation gimbal) houses the accelerometers and is held fixed in the inertial space by moving the other gimbals to counteract the vehicle motion.
A complex control system is required to generate the feedback to the torque motors that move the gimbals in such a way as to maintain the inertial integrity of the stable member. Several schemes have been developed which use classical control techniques to derive this feedback. State variable methods introduce a completely new approach which offer a more analytically appealing solution, increased design flexibility and improved performance. The function of an all-attitude gimbal assembly controller is twofold: (1) to stabilize the reference platform in inertial space, and (2) to prevent the gimbal assembly from assuming a gimbal lock geometry i.e., when all the gimbal axes are in the same plane.
Gyroscopes that are mounted on the inertial platform (stable member) of the gimbal assembly produce voltages proportional to the platform perturbation along their respective axes. Three orthogonal gyroscopic errors; the V-gyro, J-gyro and R-gyro errors; are generated from these voltages. Moving the gimbals to null the three orthogonal gyro errors isolates the stable member from vehicle motion. "Gimbal lock" refers to the undesirable situation in which all four gimbal axes are coplanar. When the gimbal assembly is in a lock configuration, there are vehicle motions that cannot be isolated from the inertial platform by torquing the gimbals, resulting in the loss of the inertial reference. As described above, optimal state variable methods introduce a completely new approach which offers a more analytically appealing solution, increased design flexibility and improved performance. Referring to block diagram, the system to be stabilized by the state variable method is a subsystem of the complete gimbal assembly. Specifically, in the absence of friction, the V-gyro and J-gyro errors are almost zero and the inner elevation gimbal torques are virtually isolated from the rest of the gimbal assembly. The small V-gyro and J-gyro disturbances that are produced by the intergimbal friction and less significant effects are corrected by closing simple single-input single-output servos around these errors.
The feedback torques to the middle and outer gimbals are computed using cost function minimizing (cost-optimal) state variable methods. The number of computations to be performed for the middle and outer gimbal state variable control is very large as the cost function minimizing optimal feedback matrix F.sub.o must be generated by performing a large number of mathematical operations on the values of inner gimbal and middle gimbal angles, A.sub.i and A.sub.m, respectively. Thus, there is a need for a cost-optimal state variable method which does not involve inordinate amount of computational requirements beyond the capability of vehicle onboard control processors.